Question : A and B can do a piece of work in 36 days. B and C can do the same work in 60 days. A and C can do the same work in 45 days. In how many days can B alone complete the same work?
Option 1: 45
Option 2: 60
Option 3: 90
Option 4: 120
Correct Answer: 90
Solution :
Let the rates at which A, B, and C can complete the work as
These rates are the reciprocals of the time it takes each person to complete the work.
From the problem,
Adding these three equations,
From equation (3) and (4),
The time it takes for B to complete the work alone is the reciprocal of B's rate =
Hence, the correct answer is 90.
